On the Equivalence of the Stability of the D-E and J-E ADE-FDTD Schemes for Implementing the Modified Lorentz Dispersive Model

Abstract

Recently, the stability of the D-E and the J-E auxiliary differential equation (ADE) schemes, which are used in implementing the modified Lorentz dispersive model in the finite difference time domain (FDTD) algorithm, has been studied by Prokopidis and Zografopoulos and it has been concluded that "the J-E implementation is proven more restrictive compared to D-E" and "the D-E implementation is more robust in terms of stability," In order to avoid drawing inaccurate conclusions regarding the J-E ADE-FDTD scheme in general, it is shown in this comment that if the bilinear frequency approximation technique is used in the FDTD discretization of the J-E ADE scheme, one can obtain the same stability polynomial as that of the D-E ADE scheme, and therefore, the same stability conditions will be applied. Hence, the stability limitations of the ADE scheme are based on the FDTD discretization methodology rather than the ADE-method itself. Finally, a numerical example carried out in a one-dimensional domain shows that the presented J-E ADE implementation is numerically stable as well as accurate as the D-E ADE counterpart.Index Terms-Auxiliary differential equation (ADE), bilinear frequency approximation, finite difference time domain (FDTD), modified Lorentz model, Routh-Hurwitz, stability analysis, von Neumann.

An FDTD method for multiterm modified Lorentz media and comparisons with existing schemes

“…as already proposed in Ramadan 19 and Prokopidis and Zografopoulos, 20 denoted here as J-E(2). The relative numerical permittivity for this scheme can be obtained similarly and it is given by ( 16) as of the proposed scheme.…”

“…The stability of the above scheme, denoted in the following as J‐E(1), was studied in Prokopidis and Zografopoulos 8 and a similar method can be formulated with less restricted stability criterion $$$\left(\frac{{b}_{2}{\delta }_{t}^{2}}{{\rm{\Delta }}{t}^{2}}+\frac{{b}_{1}{\delta }_{t}{\mu }_{t}}{{\rm{\Delta }}t}+{b}_{0}{\mu }_{t}^{2}\right){{\bf{J}}}^{n}={\varepsilon }_{0}\left(\frac{{a}_{1}{\delta }_{t}^{2}}{{\rm{\Delta }}{t}^{2}}+\frac{{a}_{0}{\delta }_{t}{\mu }_{t}}{{\rm{\Delta }}t}\right){{\bf{E}}}^{n},$$$ as already proposed in Ramadan 19 and Prokopidis and Zografopoulos, 20 denoted here as J‐E(2). The relative numerical permittivity for this scheme can be obtained similarly and it is given by () as of the proposed scheme.…”

One-Step Crank-Nicolson Direct-Splitting Algorithm with Enhanced Absorption to Evaluate Low-Pressure Discharge for Satellite Sensors in Outer Space

“…According to the physics of plasma, it can be expressed by the Lorentz medium in the finite-difference time-domain (FDTD) algorithm [ 8 ]. The Lorentz medium can be solved by the piecewise linear recursive convolution scheme (PLRC), trapezoidal recursive convolution scheme (TRC), JE convolution (JEC) scheme and so on [ 9 , 10 , 11 , 12 ]. Among them, it has been testified that the PLRC method shows the most considerable accuracy [ 13 ].…”

A Precise-Integration Time-Domain Formulation Based on Auxiliary Differential Equation for Transient Propagation in Plasma

“…The most frequently used FDTD methods can be categorized into three types: the recursive The associate editor coordinating the review of this manuscript and approving it for publication was Muhammad Zubair . convolution (RC) method [12]- [14], the auxiliary differential equation (ADE) method [15]- [17], and the Z-transform (ZT) method [18]- [21]. These algorithms based on the FDTD method have two significant problems, the limit of the Courant-Friedrich-Levy (CFL) condition and the increasing numerical dispersion error, which have limited the intense utilization of the FDTD method as the problem size expands.…”